Logic, parts of which form a branch of mathematics and parts of which form a branch of philosophy, is the science of reasoning. This course covers the classic core of what is known as intermediate mathematical logic (IML). IML includes basic computability theory (Turing Machines and other simple automata, the halting problem, the busy beaver function, Church's Thesis, etc.), the ``big" theorems setting out the main meta-properties of the propositional and predicate calculus (such as soundness, completeness, undecidability; these theorems are themselves bound up with computability), and uncomputability (which pertains to the limits of computation, and what is beyond those limits). IML also specifically includes Gödel's incompleteness theorems, and in fact these results will be presented as a theme in this course. (At the start of the course we'll consider abstract versions of Gödel's first incompleteness theorem.) Uncomputability will also be emphasized.
While I find IML interesting in its own right, one of IML's main attractions for me is that it provides a comprehensive mathematical framework for studying and perhaps replicating minds and machines. Accordingly, this course will include references to Artificial Intelligence and Cognitive Science.